Item Selection By “Hub-Authority” Profit Ranking Ke Wang Ming-Yen Thomas Su Simon Fraser University

Item Selection By “Hub-Authority” Profit Ranking Ke Wang Ming-Yen Thomas Su Simon Fraser University

Ranking in Inter-related World Web pages Social networks Cross sellings

$1.5 $10 $3 $0.5 $5 $3 $15 $2 $8 100% 30% 50% 35% 60% Item Ranking with Cross-selling Effect What are the most profitable items?

The Hub/Authority Modeling Hubs i: “introductory” for sales of other items j (i->j). Authorities j: “necessary” for sales of other items i (i->j). Solution: model the mutual enforcement of hub and authority weights through links. –Challenges: Incorporate individual profits of items and strength of links, and ensure hub/authority weights converges

Selecting Most Profitable Items Size-constrained selection –given a size s, find s items that produce the most profit as a whole –solution: select the s items at the top of ranking Cost-constrained selection –given the cost for selecting each item, find a collection of items that produce the most profit as a whole –solution: the same as above for uniform cost

Solution to const-constrained selection # of items selected Optimal cutoff Estimated profit Selection cost

Web Page Ranking Algorithm – HITS (Hyperlink-Induced Topic Search) Mutually reinforcing relationship –Hub weight: h(i) =  a(j), for all page j such that i have a link to j –Authority weight: a(i) =  h(j), for all page j that have a link to i h(j) a and h converge if normalized before each iteration

The Cross-Selling Graph Find frequent items and 2-itemsets Create a link i  j if Conf(i  j) is above a specified value (i and j may be same) “Quality” of link i  j: prof(i)*conf(i  j). Intuitively, it is the credit of j due to its influence on i

Computing Weights in HAP For each iteration, –Authority weights: a(i) =  j  i prof(j)  conf(j  i)  h(j) –Hub weights: h(i) =  i  j prof(i)  conf(i  j)  a(i) Cross-selling matrix B –B[i, j] = prof(i)  conf(i, j) for link i  j –B[i, j]=0 if no link i  j (i.e. (i, j) is not frequent set) Compute weights iteratively or use eigen analysis Rank items using their authority weights

Example Given frequent items, X, Y, and Z and the table We get the cross-selling matrix B: prof(X) = $5 conf(X  Y)= 0.2conf(Y  X)= 0.06 prof(Y) = $1 conf(X  Z)= 0.8conf(Z  X)= 0.2 prof(Z) = $0.1 conf(Y  Z)= 0.5conf(Z  Y)= XYZ X Y Z e.g. B[X,Y] = prof(X)  conf(X,Y) =

Example (con’t) prof(X) = $5, prof(Y) = $1, prof(Z) = $0.1 a(X) = 0.767, a(Y) = 0.166, a(Z) = HAP Ranking is different from ranking the individual profit –The cross-selling effect increases the profitability of Z

Empirical Study Conduct experiments on two datasets Compare 3 selection methods: HAP, PROFSET [4, 5], and Naïve. HAP generate the highest estimated profit in most cases.

Empirical Study Drug StoreSynthetic Transaction #193,99510,000 Item #26,1281,000 Avg. Trans length Total profit$1,006,970$317,579 minsupp0.1%0.05%0.5%0.1% Freq. items Freq. pairs

Experiment Results *PROFSET[4]

Experiment Results (con’t)